This proposal is for an investigator initiated multicenter clinical trial of medical/surgical therapy to prevent stroke in asymptomatic patients with stenosis of the distal common and/or internal carotid artery. There are two components - a surgical and a medical. Surgical. The major aim of the surgical component is to compare the effectiveness of aspirin + endarterectomy versus aspirin alone in reducing the incidence of TIA and cerebral infarction in patients with asymptomatic hemodynamically significant stenosis of the carotid artery. A secondary objective is to determine the incidence of recurrent stenosis following carotid endarterectomy. Medical. The major aim of the medical component is to compare the effectiveness of aspirin versus ibuprofen versus a placebo in reducing the incidence of the primary endpoints of TIA, cerebral infarction, or progression to hemodynamically significant stenosis in patients with asymptomatic non-hemodynamically significant stenosis of the carotid artery. An important secondary aim is to make such a comparison in terms of the secondary endpoint of myocardial infarction or other cardiac ischemia in those patients with no such symptoms. Another secondary objective is to determine the relationship of the progression of carotid stenosis (from non-hemodynamically significant to hemodynamically significant) to the occurrence of cerebral ischemia (TIA or stroke). In the surgical component, follow-up will be for a minimum of five years and will evaluate the frequency and magnitude of subsequent neurological events and the recurrent stenosis rate at the operated site. In the medical component, follow-up will also be for a minimum of five years to evaluate the development of neurological symptoms and the rate of progression of stenosis as assessed by noninvasive studies.